Abstract
In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature—whistler drift modes that propagate along the electron drift as a Burger’s shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral—are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.
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